5. Di-tau mass estimation 53
6.6. Systematic Uncertainties
Systematic uncertainties are related to both theoretical and experimental sources and are described in this section.
6.6.1. Experimental Uncertainties
The experimental uncertainties are estimated using the Moriond 2017 recommendations provided by the ATLAS Combined Performance groups. The objects related uncertain-ties are:
• Electron/Muon uncertainties [92]:
– Resolution : variations related to ID (electron/muon) and MS tracks (muon only);
– Scale : variation of the momentum scale;
– Efficiency : statistical and systematic uncertainties for trigger efficiency, iden-tification efficiency and isolation efficiency; reconstruction efficiency is consid-ered only for electron.
• Tau uncertainties:
– Scale: variation of the energy scale due to the modelling of the detector geom-etry, measurement performed in tag-and-probe analysis and Geant4 physics list;
– Efficiency : efficiency uncertainties due to the τ identification, reconstruc-tion, electron overlap removal performed independently for true electrons and hadronically decaying taus.
• Jet uncertainties [93]:
– Resolution : the jet resolution uncertainty is parametrised using an 11 nui-sance parameters scheme; this scheme expects also data smearing in order the derive the final uncertainty which should be applied on the Monte Carlo samples;
– Scale : the jet scale resolution is parametrised using a 21 nuisance parameters scheme;
– Efficiency : efficiency uncertainties for the jet vertex tagger which is applied both in the central and the forward part of the detector.
Further source of jet related uncertainties is due to the b-tagging which is used to reject (enhance) Top contribution in the signal (control) regions.
• ETmiss uncertainties:
The uncertainty on the ETmiss calculation using track-soft terms calculated from the total transverse momentum of the hard objects (electrons, muons, jets and taus) reconstructed in the event; this was evaluated by comparing data taken in 2015 and 2016 with Monte Carlo simulations [93].
• Pileup re-weighting:
Since Monte Carlo simulation was performed using a generalized profile for the distribution of the number of interactions per bunch crossing, the simulated events have to be re-weighted to describe the observed pileup profile for the 2015 and 2016 datasets. To get the best agreement between data and Monte Carlo simu-lation, a correction factor of 1/1.16 needs to be applied to the simulated number of interactions. The uncertainty at 1 σ level is given by 1/(1.16±0.07), however it was recommended to use the more conservative value of 1/(1.16+0.07−0.16) as it was done in this analysis.
• Luminosity uncertainty:
The uncertainty on the combined 2015 and 2016 luminosity is 2.9 %. This value
was derived from a preliminary calibration of the luminosity scale using x-y beam-separation scans performed in August 2015 and May 2016. This combined uncer-tainty assumes fully correlated uncertainties between the 2015 and 2016 dataset.
6.6.2. Theoretical Uncertainties
In the following section, the theoretical uncertainties forZ →τ τ and signal are discussed.
Theoretical uncertainties forZ →τ τ
The normalisation of theZ →τ τ+jets background is left free-floating in the final anal-ysis fit. Two normalisation factors are defined, controlling the overall normalisation of Z →τ τ across channels in the VBF signal regions and Boosted signal regions respec-tively. Therefore each considered source of systematic uncertainty can be parametrized using the following strategy:
• a set of nuisance parameters (one per each inclusive SR and per channel) to account for the impact of the variation on the discriminant variable as well as the event migration from a signal region to the other one within a given inclusive region. For each channel, it is evaluated after the variation has been constrained to the same normalisation as the nominal prediction in the inclusive signal regions (Boosted inclusive and VBF inclusive regions);
• two nuisance parameters (one for each inclusive SR) to account for the fact that the definition of the inclusive regions are different across the three channels (τlepτlep, τlepτhad and τhadτhad) and it can therefore be impacted differently by the given systematic uncertainties. It will be evaluated as the impact of the variation on the relative normalisation of each channel with respect to the total expectation regardless of the decay channel. It is worth to notice that these nuisance parameters are not considered in the case of a standalone fit performed using only one decay channel.
The following sources of uncertainty have been considered:
• PDF: evaluated using event-weights provided by the Sherpa MC generator;
• renormalisation and factorisation scales (µR/µF) : evaluated using event-weights provided by theSherpa MC generator;
• CKKW : jet-to-parton matching uncertainty, evaluated using truth-level parametri-sation of the jet multiplicity and pT(Z);
• resummation scale (qsf ): evaluated using truth-level parametrisation as a function of the jet multiplicity and pT(Z);
• underlying-event : evaluating using sample with different setup of multiple inter-actions. It has been found that this uncertainty has negligible impact and it was not used in the final fit setup;
• parton-shower: due to a lack of recommendations for this source of uncertainty, this has been covered comparing Sherpa and Madgraph Z →τ τ+jets MC generators.
Theoretical uncertainties for Signal
The relevant theoretical uncertainties on the SM predictions used in the analysis arise from three main sources:
• QCD scale uncertainties due to missing higher orders in perturbation theory;
• non-perturbative parts of the calculation (underlying event and hadronisation);
• uncertainty on experimental input parameters such as parton density functions (PDFs) and the value of the strong interaction coupling constant, αS.
In the final fit model, the uncertainty is based on the variations in the number of events predicted in each MMC bin :
nbin =σtot×L×A×fbin (6.8)
whereσtot is the total cross section,Lis the luminosity,Ais the acceptance of the total sample in a signal region andfbin is the fraction of events in a certain bin of the MMC distribution. The theory uncertainties are factorised into uncertainties on the total cross section, uncertainties on acceptances into the signal regions and uncertainties of the MMC shape distribution.
The total cross section uncertainties are provided by theLHC Higgs cross section Work-ing Group (LHCHXSWG) and are shown in Tables6.11and6.12, respectively for QCD, PDF and αS uncertainties.
The QCD scale uncertainties are evaluated varying the renormalisation and factorisa-tion scales µR, µF by factors 2 and 1/2 around the central value with the constraint 1/2 6 µF/µR 6 2. For the VBF and VH process, the samples are generated with Powheg+Pythia8 at NLO and the internal weights of Powheg are used for the scale variations; the envelope of these variations is then kept as final uncertainty.
For the gluon fusion Higgs production a simple variation of the factorisation and renor-malisation scales is not sufficient. Due to accidental cancellations in the perturbative calculation, the variation of the renormalisation and factorisation scales underestimates the uncertainties. For this reason, QCD scale uncertainties for gluon fusion need a spe-cific treatment and 9 sources of uncertainties related to the truncation of the perturbative series are recommended:
• 4 scale variations uncertainties:
– ∆µ: factorisation and renormalisation scale variations;
– ∆φ: resummation scale variation;
– ∆0/1cut(∆1/2cut) : 0 ⇐⇒ 1(1 ⇐⇒ 2) jet bin migration.
• 2 VBF topology uncertainties:
– variation of the VBF phase space;
– 3rd jet veto.
• 2 Higgs pT-shape uncertainties:
– Higgs pT 0-60/60-∞ GeV;
– Higgs pT 0-120/120-∞GeV.
• 1 top mass dependent uncertainty.
The first four variations are established using the method described in the Yellow Report 4 [94], the two VBF topology uncertainties are derived using Yellow Report 3 [29] meth-ods, the Higgs pT shape variations are taken from the QCD scale variations of Powheg NNLOPS and the last uncertainty, related to the top mass, is derived from differences between LO and NLO rescaling.
Parton shower uncertainties are evaluated comparing two parton shower algorithms, Pythia8 and Herwig7; to do this, two samples for each channel and production mode were produced using ATLAS Fast simulation samples. It is worth to mention that these samples suffer from a lack of statistics and probably should be replaced with larger statistics samples.
PDF uncertainties are evaluated according to the most recent recommendations of the PDF4LHC collaboration: the used PDF set consists of 30 eigenvector variations and 2 variations ofαS which are then statistically combined as independent nuisance parame-ters in the fit.
Production process + QCD scale - QCD scale
ggH +3.9 % -3.9 %
VBF +0.4 % -0.3 %
WH +0.5 % -0.7 %
ZH +3.8 % -3.1 %
Table 6.11.:Total cross section uncertainties due to missing higher orders (QCD scale varia-tions) from YR4 of the LHCHXSWG.
Production process PDF αs (PDF +αs)
ggH ±1.8 % ±2.5 % ±3.1 %
VBF ±2.1 % ±0.5 % ±2.1 %
WH ±1.7 % ±0.9 % ±1.9 %
ZH ±1.3 % ±0.9 % ±1.6 %
Table 6.12.:Total cross section uncertainties due to PDFs and αs from YR4 of the LHCHXSWG.